The most important topic of the day is graphing quadratic
equations of the form y = ax2 + bx+ c ,
like the three be low . We’ll begin by using the old-fashi oned method of plotting
points and
connecting the dots.
Unless you’re blind as a bat or have sushi for brains, you
will notice that all three graphs have the
same basic shape. This U-shaped graph is called a parabola, and every
quadratic equation has a
graph with this shape. Some open upward, some downward. The turning point can be
pretty much
anywhere, and some are thin, and some are wide.
Some terms associated with parabolas:
Vertex –
Symmetric –
Axis of Symmetry –
The key to graphing a parabola is finding the vertex , and we can easily develop
a formula for doing
that in the space below.
So to find the vertex of a parabola (in the form y = ax2
+ b x+ c, you…
1) Use the formula x = − b/2a . This is NOT THE ANSWER! The vertex is a POINT on
the
graph; this formula provides a number . It tells us the FIRST coordinate of the
vertex .
2) To find the second coordinate, plug the first coordinate you found back into
the equation
and find y. The make sure to write the vertex as an ordered pair , like (0, 4)
for the second parabola
graphed above.
Now we can out line a simple procedure for graphing every quadratic equation with
no help from a
graphing calculator :
1) Find the vertex.
2) Find at least one more point on each side of the vertex.
3) Draw the parabola , keeping in mind that it has to be symmetric on either side
of the
vertex.
Examples:
y = −x2 − x + 2
Find vertex and at least two other points:
y = x2 −2x −8
Find vertex and at least two other points:
y = −16x2 +64x
Find vertex and at least two other points:
Helpful point: What about the equation determines whether
the parabola opens up or down?
(Knowing this can help you to check your graph after you’ve found points on each
side of the vertex)
HW: p. 646: 11-19 odd; 27-33 odd; 41-49 odd. For any problem that asks you to
graph a quadratic
equation, ignore their directions and use the procedure outlined on page 3 of
this document.
